Theorem 2 ([1]}) 
Let \(G\)  be a graph, and let \(X_1\) , \(X_2\)  and \(Y=V(G)\setminus (X_1\cup X_2)\)  be three disjoint nonempty subsets of \(V(G)\) . Suppose that each largest subset of arcs with the same label of \([X_1,Y]\)  arc-induces a complete bipartite subgraph of \(G\) , each largest subset of arcs with the same label of \([Y,X_2]\)  arc-induces a complete bipartite subgraph of \(G\) , the arcs of \([X_1,X_2]\)  have no labels in common with any arc in \([X_1,Y]\cup [Y,X_2]\) , and the arcs of \(G/X_1/X_2\)  and \(G/Y\)  corresponding to the arcs of \([X_1,Y]\cup [Y,X_2]\cup [X_1,X_2]\)  are the only synchronising arcs of \(G/X_1/X_2\)  and \(G/Y\) .
If \(S^{\prime }(G)\subseteq X_1\) , and \([X_1,Y]\) , \([Y,X_2]\)  and \([X_1,X_2]\)  have no backward arcs, then \(G\cong G/YG/X_1/X_2\) .

